Rukasha Maths

GCSE maths Beta

Algebraic fractions and rearranging formulae · Revision guide

Higher · Algebra · 1 page in the PDF

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Learning objectives

  • Simplify and add algebraic fractions while retaining excluded values.
  • Rearrange a formula by collecting and factoring the required subject.

Key ideas

Record original denominator exclusions before cancelling.

denominator≠0\text{denominator}\ne0

Cancel common factors, never separate terms of a sum.

abac=bc(a≠0, c≠0)\frac{ab}{ac}=\frac bc\quad(a\ne0,\ c\ne0)

Use a common denominator to add or subtract.

If the subject appears twice, collect its terms, factor, then divide by a non-zero factor.

Worked examples

Example 1

Simplify the fraction and state its excluded values.

x2−9x2+3x=(x−3)(x+3)x(x+3)\frac{x^2-9}{x^2+3x}=\frac{(x-3)(x+3)}{x(x+3)}

The original denominator must stay non-zero.

x≠0,x≠−3x\ne0,\qquad x\ne-3
x−3x,x≠0,−3\frac{x-3}{x},\qquad x\ne0,-3

Example 2

Add the fractions using a common denominator.

1x+1x+1=x+1+xx(x+1)\frac1x+\frac1{x+1}=\frac{x+1+x}{x(x+1)}
2x+1x(x+1),x≠0,−1\frac{2x+1}{x(x+1)},\qquad x\ne0,-1

Watch out

Cancelling a factor does not remove its original excluded value. Keep every original denominator non-zero.